The angular velocity of a fan blade is 4.6 radians per second.

Approximately how many revolutions does the fan blade make in 2.4 minutes?

State your answer, rounded to the nearest tenth of a revolution.

In 2.4 minutes the fan made 105.5 revolutions.

Step-by-step explanation:

In order to solve this problem we need to convert the speed from radians to revolutions. To do that we can use a rule of three as shown below:

2pi rad/s - > 1 rev/s

4.6 rad/s - > x rev/s

2pi/4.6 = 1/x

2pix = 4.6

x = 4.6/2pi = 2.3/pi rev/s

Now we need to conver the time at which the blade was spinning from minutes to seconds, to do that we need to multiply by 60.

t = 2.4*60 = 144 s

To calculate the number of revolutions we multiply the angular velocity of the fan by the time it was spinning:

rev = (2.3/pi) * 144 = 331.2/pi = 105.5 revolutions

105.4 revolutions

Step-by-step explanation:

By converting 2.4 min into seconds, we'll have

2.4 minutes = 60 x 2.4 = 144 seconds.

Now, in 2.4 minutes, the fan rotate 4.6 [rad/s] x 144s = 662.4 radians

As the answer is required in revolution

therefore, 1 radian = 0.159155 revolutions

so 0.159155 x 662.4 = 105.4 revolutions

The fan rotated 105.4 revolutions in 2.4 minutes